Britney and Madonna, you may want to take note. That young kook Chloë Sevigny shaved her head while she was still in high school and had a contract with H&M before she was out of her teens. It seems there is not much that this remarkable young actress hasn’t already set a template for. From her role as the HIV-infected heroine in Larry Clark’s Kids through her infamous fellatio scene in The Brown Bunny to playing a polygamous wife of a Mormon sect member in Big Love, Sevigny has cleaved to the offbeat, the tangential and the oblique.

‘Most of the films I’ve decided to do I’ve chosen because of the director. Perhaps now I should focus on finding meatier roles,’ she says. ‘I always feel like it’s a collective when you’re making a movie. It’s a collaboration between hundreds of people that are all doing their little bits. And I’m okay to play the little supporting part as long as it serves the good of the movie and it’s a great director or a great script or something I’m really excited about.’

Which explains why Sevigny accepted a part in Zodiac, director David Fincher’s true crime thriller, which, at first glance, doesn’t seem an obvious choice for the 32-year-old actress. Fincher, the man behind Se7en, Panic Room, Fight Club and Aliens 3, was growing up in San Francisco when the Zodiac killer was terrorising the area. He describes making the film as a ‘massive personal undertaking’ to tell the true story of one of America’s most notorious serial killers who taunted police authorities in four jurisdictions with his handwritten ciphers and letters to the San Francisco Chronicle in the 60s, 70s and 80s.

Zodiac stars Jake Gyllenhaal as real life San Francisco Chronicle cartoonist Robert Graysmith who, along with three other men (played by Robert Downey Jr, Mark Ruffalo and ER’s Anthony Edwards), became obsessed with capturing the killer, to the detriment of their own health. Sevigny plays Gyllenhaal’s dour but strong wife Melanie.

‘I read Zodiac the book before we started shooting. It was frightening, sitting at home alone reading these horrible crime scenes.

‘What I like about Melanie is the respect she had for her husband. And even though she couldn’t agree with what he was doing she respected him enough to let him do it. She was probably kind of interested in what her husband was into and learning about it, but ultimately he was putting their lives in danger for the sake of what? What is he going to get out of this? Why is he obsessed with this? Is he going to bring him down? He’s not going through the regular channels and that’s part of the frustration of the movie.’

Sevigny is the first to admit that masters of what can best be described as ‘effortless minutiae’ have honed her best work. They include Jim Jarmusch (who gave her a small part in Broken Flowers), and Whit Stillman (who gave her one of her first big roles in 1998 with The Last Days of Disco).

Given her love of a challenge, she was eager to work with Fincher, a director renowned for his exacting standards, who thinks nothing of notching up 100 takes to get a scene just right. She concedes she shares a little of Fincher’s obsession. ‘My first day was, I think, 80 takes. It was a two-shot of Jake and I in a phone booth in the rain on the street in San Francisco. And there was a big camera move, and we both had to have our performances just right. And the rain had to be right and the light had to be right and the cars had to be right and the extras had to be right, and the camera move had to be right. It wasn’t only performance. It was that a lot of elements had to be just right. And he would watch back every single take.’

Warming to her subject Sevigny adds, ‘But you know I am obsessive like Fincher. I like that he was a complete control freak, because then I didn’t have to worry about being in control of anything because I knew that he was. I love that about him. In between each take, if you were drinking a glass, he would have someone come with a ruler and measure how much liquid was in your glass between each take, to make sure it was back to the same, and I was like, “Yeah, I like that.” I love the art of filmmaking and that’s why I love this movie. There’s craftsmanship on every level of this film; it is impeccable.’

Ever since her childhood in Darien, Connecticut, Sevigny (the daughter of a Polish American mother and distantly descended French aristocratic accountant-turned-interior designer father) has walked an enviably cool line. Her first taste of fame came when she was spotted at a newspaper kiosk by Mary Clarke and Andrea Lee Linett, the fashion editors of then cult teen fashion magazine Sassy, who put the teenager to work as an intern and occasional model. She then inspired Jay McInerney to write an article about her for The New Yorker in which he described her as ‘the coolest kid in the world’.

After a chance encounter with writer and fellow skateboarder Harmony Korine led to a part in 1995’s Kids, she went from being a thrift-store Tinkerbell to couture fashion muse (Louis Vuitton, Marc Jacobs, Dolce and Gabbana and YSL). Next came acting awards and an Oscar nomination, at the age of 25, for Boys Don’t Cry. Sevigny also became the performer of the world’s second most famous act of fellatio, in Vincent Gallo’s 2003 film The Brown Bunny (she will always have to wait in line behind a certain Monica Lewinsky).

Guided by a precocious feel for good material and interesting filmmakers she has notched up a roster of highly commendable if largely commercially underperforming independent films. When mention is made of her lack of commercial success since the Oscar winning Boys Don’t Cry, she positively bursts with explanation: ‘I had a lot of offers and a lot of movies that were meant to happen after Boys Don’t Cry that were great, great scripts and great directors and on two of them, the leading men broke limbs. So, they fell apart. They both would’ve been really great for me, but I’m glad to still actually be struggling. I enjoy the struggle.’

Last year UK television audiences saw her in US cable station HBO’s feted Mormon community drama Big Love. In it she plays Nicolette, second wife of Bill Paxton’s polygamist prophet Bill Hendrickson. ‘It’s a great part. I love the show,’ she enthuses. The second series is due out in America this summer while a UK date is so far unconfirmed. Her character is arguably the most conservative of the wives and Sevigny insists that she is far more conservative in real life than her persona might suggest.

By way of squaring some bizarre cultural circle, the actress is currently gearing up to play Catherine II (the Great) in Polish filmmaker Agnieszka Holland’s epic biopic Catherine and Peter. Sevigny’s late father’s connection to 17th Century aristocrat (and great lady of letters) the Marquise de Sevigney may have been tenuous, but undoubtedly has the coolest of blue blood running through it. Sevigny is handsome and pretty, but she may also be the real queen of New York City.

Zodiac is on general release from Fri 18 May